Mathematicians like Stanley Osher, Yves Meyer, Daniel Spielman and Alberto Adrego Pinto are examining areas of life where maths can find applications, including modelling of human behaviour, writes Kalyan Ray

Mathematics can very well trigger a multi-billion dollar spectacle. Ask James Cameron if you don’t believe. The world’s biggest money-grossing movie, Avatar, would not have been a reality without some complicated mathematics.

The same maths that made the Na’vis’ struggle on Pandora so real could also be used to locate a terrorist hide-out and give out a better scan even though the patient had to stay for a few fleeting seconds inside an MRI machine.

Meet Stanley Osher, one of the best-known brains in applied mathematics from the University of California, Los Angeles, who pioneered such mathematics. Over the years, he has researched on a new area of mathematics called ‘level set methods’, which is a way of determining how surfaces such as bubbles move in three dimensions and how they merge and so on. Though on the face of it, LSM appears to be a subject of academic interest, Osher and his graduate students Ron Fedkiw found its utility in computer graphics. The maths also found its way to Hollywood.

Ants was the first movie that used LSM-based graphics, followed by films like Terminator. But computer graphics touched a new height with Cameron’s sci-fi epic, all set for a global re-release with nine minutes of additional footage. “Our method was used extensively to create the graphics for Avatar. It was used to make water, hills and fires in the movie. Most of the Hollywood studios like Disney and Columbia Tristar use our technology,” Osher told Deccan Herald at the International Congress of Mathematicians that ended in Hyderabad on August 27.

In fact, Cameron’s earlier blockbuster Titanic was probably the last well known film that used old-fashioned technologies. The water in Titanic did not come out well, he said, adding that the LSM offered a much more simplified model to mimic the natural world more accurately. Osher – who describes himself as the world’s best analyst among the current lot – doesn’t have much time to look for more innovative applications in the movies, which he describes as the fake world. The real world of military and medical imaging attracts him more.

Maths in real life

For the military, applied mathematics comes handy in detecting IED (improvised explosive device) from space. For the medical community, it means subjecting a patient under less radiation exposure in an MRI or CT machine but still getting an improved scan. The 68-year old mathematician is using maths for practical applications for many years. It began with the infamous Los Angeles riot in 1993 when the city went up in smoke triggered by the Rodney King incident. One of the cases involved a truck driver, Denny, who was at the receiving end of one attack. A video image taken from a helicopter revealed a speck on the arm of a person throwing a brick at Denny. Osher who was doing video image analysis with his colleague L Rudin resolved the speck into a rose tattoo, leading to the conviction of the suspect. But Osher is among a rare breed of mathematicians whose work has a direct and immediate bearing in the real world. Most mathematicians work in esoteric areas with complicated concepts and admit that their work has no immediate practical applications. Actually it can take several decades before new concepts in higher mathematics found an application.

Meyer’s maths

Take the research of Yves Meyer, professor emeritus at Ecole Normale Superieure de Cachan in France for example. Winner of the Gauss prize in the ICM, 2010, Meyer made many fundamental contributions to several areas in mathematics. The applications came over a decade later. Meyer’s work forms the basis of the common photograph standard JPEG-2000 and restoration of satellite imagery.

More recently, one of Meyer’s early work – known as Meyer Sets – was exploited to process the images beamed by European Space Agency’s Herschel space probe that aims to photograph some of the universe’s oldest and coldest stars in the universe. Being some of the coldest stars, they emanate very faint light necessitating the requirement for a new algorithm to process even those faint lights. Meyer’s 1970 work was used to make sense of it.

“Mathematics is an exciting place as there are applications from academics to industry,” said Daniel Spielman of Yale University, USA. Spielman who bagged the 2010 Rolf Nevanlinna prize for outstanding contribution to the mathematical aspect of information sciences, thanked his Grade-4 teacher for fuelling his interest in maths.

While the information sciences offer tremendous opportunities for mathematicians, Spielman whose work on error correcting code has made the online credit card transaction secure, said new opportunities are opening up in system biology, drug development and even in social areas like economy and political science. “Mathematics is used to understand the unpredictable nature of the financial market,” said Alberto Adrego Pinto from the Universidade do Porto in Portugal. Incidentally, Pinto and his colleagues used the same type of mathematical models was to find out distribution of sun spots.

The next big challenge for mathematicians like Pinto is to model human behaviour. “It’s very complicated but we are working on it,” he admitted.

Original Link: http://www.deccanherald.com/content/92587/brains-behind-maths.html

Mathematician Stanley J. Osher, whose firms Cognitech Inc., Luminescent Inc., and Level Set Systems Inc. are all solving real world problems, says it’s an “incredible time for mathematicians”

Hyderabad: Stanley J. Osher, is not your stereotypical mathematician—serious-looking, immersed in abstraction. Having co-founded three companies in 22 years, based largely on his own research, Osher is a mathematician and an entrepreneur, who, in a plenary lecture on 25 August, is going to tell the 3,000-plus mathematicians gathered at the International Congress of Mathematicians (ICM) in Hyderabad how “fast” algorithms are going to rock the world.

Osher, whose firms Cognitech Inc., Luminescent Inc., and Level Set Systems Inc. are all solving real world problems, says it’s an “incredible time for mathematicians”. His and others’ work in “level set” theorems, which enable capturing moving images into math models, have led to applications that were unthinkable before.

“The whole industry of graphics in movies is using these algorithms,” says Osher, director of applied mathematics at the University of California in Los Angeles. Titanic was the last movie to use old-fashioned technology of simplified physical models. The special effects of the recent 3D movie Avatar owe their brilliance to level-set algorithms, he adds.

Osher’s message to mathematicians isn’t formulaic: fast algorithms can analyse data in a variety of sectors, from better medical imaging with reduced radiation dosage to spectral imaging in military applications.

In the financial world, quants have already shown what analytics can do. Now, say experts, it’s other businesses, from advertising to banking, that are increasingly relying on math to understand consumer behaviour.

This year’s Rolf Nevanlinna Prize winner Daniel Spielman of Yale University, whose interest lies at the intersection of computer science and mathematics, has also designed “fast” algorithms. His work on “error correcting codes” (ECC), which leads to better ways of transmitting and storing digital information, led his colleagues to set up a company called Digital Fountain Inc.

In a medium where even a speck of dust can wipe out thousands of bits of data, says Spielman, ECC ensures safety by adding redundancy.

What Osher and Spielman epitomize is the applied side of mathematics, a discipline, which mathematician Sujatha Ramdorai at the Tata Institute of Fundamental Research in Mumbai, says is “totally missing from the Indian mathematics community, focused as it is on pure math”.

“We need to have these new fields, at the interface of economics, social sciences and biology,” says Ramdorai.

Incidentally, even applying mathematics to studying human behaviour or financial market hasn’t caught the imagination of mathematicians in India. It’s a branch of science that Alberto A. Pinto’s research, to be presented at ICM, represents very well. Work by Pinto, a mathematician at the University of Porto, Portugal, shows how models can simulate group behaviour—a tool that can help authorities to track social deviants, and, say, prevent a riot or a terrorist attack.

Another of Pinto’s models looks at stock market indices and provides a “probability distribution of market returns”. The genesis of this model lies in the probability distribution found in the natural world, such as in sunspots or in river heights, which Pinto found to be same as in stock market indices.

Math today has direct applications and the Indian community needs figureheads such as Osher, Spielman or Pinto, says Ramdorai. “I think the (new) Indian Institutes of Science Education and Research are the best places to start such disciplines,” she adds and as a former member of the National Knowledge Commission, she has recommended this to the government.

As mathematicians get their hands on flows of data, using algorithms to model people as shoppers, voters and workers, many, if not most, experts gathered in Hyderabad say it’s a great time to be a math graduate. Osher refers to a recent survey in the US, published in The Wall Street Journal, where mathematicians ranked the highest in terms of job satisfaction.

Mathematician G. Rangarajan of the Indian Institute of Science says not a week passes by when he doesn’t get a call from some financial services firm looking for math postgraduates or doctorates. “We just need to get more students and faculty in math,” he adds.

So much for applied math and the way it’s hitched to business. But can math ever solve the larger question of consciousness? Or, model human evolution?

Stanislav Smirnov, one of the winners of 2010 Fields Medal, says it is conceivable to think mathematicians can model evolution: earlier, biologists constructed the tree of life by hand, now they use computation.

However, it’s in the understanding of another puzzling problem—human consciousness—that mathematicians seem to give up.

“It’s beyond our wildest dreams. Since there’s no way of detecting or defining it (consciousness), it remains beyond the scope of math,” says Spielman.

But Smirnov doesn’t seem to have given up entirely and wonders “if there’s an abstract explanation” for consciousness. “(An) abstract explanation means you can apply mathematics,” he says.

Seema Singh
seema.s@livemint.com

http://www.livemint.com/2010/08/24001310/Math-becomes-fashionable-focu.html?h=A1

International Congress of Mathematicians (ICM) in Hyderabad Home Page
http://www.icm2010.org.in/